implement rat in maze algorithm. (#2106)

* implement rat in maze algorithm.

* style changes

* fix trailing whitespace

* add test, fix style

* fix style

* method change

* minor changes

* style changes

* return solved

Co-authored-by: Christian Clauss <cclauss@me.com>

backtracking/rat_in_maze.py

@@ -0,0 +1,113 @@
+def solve_maze(maze: list) -> bool:
+    """
+    This method solves rat in maze algorithm.
+    In this problem we have n by n matrix and we have start point and end point
+    we want to go from source to distination. In this matrix 0 are block paths
+    1 are open paths we can use.
+    Parameters :
+        maze(2D matrix) : maze
+    Returns:
+        Return: True is maze has a solution or False if it does not.
+    >>> maze = [[0, 1, 0, 1, 1],
+    ...         [0, 0, 0, 0, 0],
+    ...         [1, 0, 1, 0, 1],
+    ...         [0, 0, 1, 0, 0],
+    ...         [1, 0, 0, 1, 0]]
+    >>> solve_maze(maze)
+    [1, 0, 0, 0, 0]
+    [1, 1, 1, 1, 0]
+    [0, 0, 0, 1, 0]
+    [0, 0, 0, 1, 1]
+    [0, 0, 0, 0, 1]
+    True
+
+    >>> maze = [[0, 1, 0, 1, 1],
+    ...         [0, 0, 0, 0, 0],
+    ...         [0, 0, 0, 0, 1],
+    ...         [0, 0, 0, 0, 0],
+    ...         [0, 0, 0, 0, 0]]
+    >>> solve_maze(maze)
+    [1, 0, 0, 0, 0]
+    [1, 0, 0, 0, 0]
+    [1, 0, 0, 0, 0]
+    [1, 0, 0, 0, 0]
+    [1, 1, 1, 1, 1]
+    True
+
+    >>> maze = [[0, 0, 0],
+    ...         [0, 1, 0],
+    ...         [1, 0, 0]]
+    >>> solve_maze(maze)
+    [1, 1, 1]
+    [0, 0, 1]
+    [0, 0, 1]
+    True
+
+    >>> maze = [[0, 1, 0],
+    ...         [0, 1, 0],
+    ...         [1, 0, 0]]
+    >>> solve_maze(maze)
+    Solution does not exists!
+    False
+
+    >>> maze = [[0, 1],
+    ...         [1, 0]]
+    >>> solve_maze(maze)
+    Solution does not exists!
+    False
+    """
+    size = len(maze)
+    # We need to create solution object to save path.
+    solutions = [[0 for _ in range(size)] for _ in range(size)]
+    solved = run_maze(maze, 0, 0, solutions)
+    if solved:
+        print("\n".join(str(row) for row in solutions))
+    else:
+        print("Solution does not exists!")
+    return solved
+
+
+def run_maze(maze, i, j, solutions):
+    """
+    This method is recursive method which starts from i and j
+    and goes with 4 direction option up, down, left, right
+    if path found to destination it breaks and return True
+    otherwise False
+    Parameters:
+        maze(2D matrix) : maze
+        i, j : coordinates of matrix
+        solutions(2D matrix) : solutions
+    Returns:
+        Boolean if path is found True, Otherwise False.
+    """
+    size = len(maze)
+    # Final check point.
+    if i == j == (size - 1):
+        solutions[i][j] = 1
+        return True
+
+    lower_flag = (not (i < 0)) and (not (j < 0))  # Check lower bounds
+    upper_flag = (i < size) and (j < size)  # Check upper bounds
+
+    if lower_flag and upper_flag:
+        # check for already visited and block points.
+        block_flag = (not (solutions[i][j])) and (not (maze[i][j]))
+        if block_flag:
+            # check visited
+            solutions[i][j] = 1
+
+            # check for directions
+            if (run_maze(maze, i + 1, j, solutions) or
+                run_maze(maze, i, j + 1, solutions) or
+                run_maze(maze, i - 1, j, solutions) or
+                run_maze(maze, i, j - 1, solutions)):
+                return True
+
+            solutions[i][j] = 0
+            return False
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()